A 60 room hotel is filled to capacity every night at a rate of $40 per room. The management wants to determine if a rate increase would increase their profit. They are not interested in a rate decrease. Suppose management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. If each rented room costs $8 a day to service, how much should the management charge per room to maximize profit?
Accepted Solution
A:
Answer: to maximize profit the management must continue charging $40 per room because it will obtain a profit of $1,920 better than $1,870 if it rises the rate.Step-by-step explanation:Profit without the increase60 (number of rooms) * $40 (rate per room) = $ 2,400 costs of day to service = 60 (rooms) * $8 (costs day to service)= $480Total Profit = $2,400 - $480 = $1,920Profit with the increase55 (5 fewer than before) * 42 (rate with the increase) = $ 2,310 costs of day service 55 (rooms) * 8 ( costs day to service) = $440Total Profit = $2,310 -$440 = $1,870